Closed geodesics on orbifolds
WebUsing the theory of geodesics on surfaces of revolution, we introduce the period function. We use this as our main tool in showing that any two-dimensional orbifold of revolution homeomorphic to... WebWe characterize Riemannian orbifolds and their coverings in terms of metric geometry. In particular, we show that the metric double of a Riemannian orbifold along the closure of its codimension one stratum is a Riemannian orbifold and that the natural projection is an orbifold covering.
Closed geodesics on orbifolds
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WebHYPERBOLIC ORBIFOLDS, AND EQUIDISTRIBUTION OF CLOSED GEODESICS IN REGULAR COVERS RON MOR Abstract. We give a finitary criterion for the convergence of measures on non-elementary geometrically finite hyperbolic orbifolds to the unique measure of maximal entropy. We give an entropy criterion controlling escape of mass to … WebAug 2, 2007 · For compact Riemann surfaces, the collar theorem and Bers’ partition theorem are major tools for working with simple closed geodesics. The main goal of this article is to prove similar theorems for hyperbolic cone-surfaces. Hyperbolic two-dimensional orbifolds are a particular case of such surfaces.
WebJul 22, 2015 · It is known that the shortest non-simple closed geodesic on an orientable hyperbolic 2-orbifold passes through an orbifold point of the orbifold (Nakanishi in Tohoku Math J (2) 41:527–541, 1989 ). This raises questions about minimal length non-simple closed geodesics disjoint from the orbifold points. WebApr 27, 2015 · CLOSED GEODESICS ON ORBIFOLDS. GEORGE C. DRAGOMIR. Abstract. In this note, we prov e the existence of a closed geodesic of positive. length on any compact developable orbifold of di mension 3, 5 ...
WebFeb 27, 2006 · Using the theory of geodesics on surfaces of revolution, we introduce the period function. We use this as our main tool in showing that any two-dimensional … WebNov 20, 2014 · The answer is, as expected no. What follows is more of a proof sketch than a complete proof. Contradiction is attained in the same fashion as in Stephen M.S.'s answer.
WebJan 1, 2007 · Since any such orbifold of revolution can be regarded as a topological two-sphere with metric singularities, we will have extended …
WebOrbifolds also arise in physics as configuration spaces after one removes formal symmetries of a system, for example gauge transformations in Yang–Mills theory and coordinate transformations in general relativity [28]. There are many different ways to approach orbifolds, for example as Lie groupoids (see Remark2.1.3), length spaces (see delete user on computer windows 10WebJun 4, 2024 · Closed geodesic. A closed smooth curve on a Riemannian manifold $ M $ that is a geodesic line. A more general notion is that of a geodesic loop, i.e. a geodesic $ … ferium xt compositionWebof the S1-orbits of closed geodesics in a geometric equivalence class. In the last section, we sketch how the classical theory of closed geodesics on Riemannian man-ifolds can be adapted to the case of orbifolds. In sections 3, 4 and 5 we assume familiarity with the notions and the basic papers concerning the theory of closed ferity.czWebExistence of closed geodesics on compact manifolds was first proved by Lyusternik and Fet in the 1950s using Morse theory, and the corresponding problem for orbifolds was studied by... ferius creekWebWe shall also consider the problem of the existence of innitely many geometrically distinct closed geodesics. In the classical case the solution of those problems involve the … ferivi tech fleecehttp://arxiv-export3.library.cornell.edu/pdf/1703.00850v2 ferivi outletWebThe existence of closed geodesics on Riemannian manifolds has a long and storied past dating back to Poincar¶e [2]. It seems that not much has been done ... The existence of at least one closed geodesic on a compact 2-orbifold was shown in [7] and closed geodesics in orbifolds of higher dimensions have recently been studied in [10]. The paper ferity style pen